期刊名称：Computational Methods in Science and Technology
印刷版ISSN：1505-0602
出版年度：2018
卷号：24
期号：2
页码：159-163
DOI：10.12921/cmst.2018.0000032
出版社：Poznan Supercomputing and Networking Center
摘要：The one-dimensional φ4 Model generalizes a harmonic chain with nearest-neighbor Hooke’s-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature: because the quartic tethers act to scatter long-wavelength phonons, φ4 chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the three-dimensional energy surface describing a two-body two-spring chain. That surface can include at least two distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body φ4 problems merit more investigation. Accordingly, the 2018 Prizes honoring Ian Snook (1945-2013) will be awarded to the author(s) of the most interesting work analyzing and discussing few-body φ4 models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model’s ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.
